correlation.m

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function [R, Q, sigma_deg] = correlation(M, spacing, d_norm, ...
					 cluster_number, amplitude_cluster, ...
                     PAS_type, phi_deg, AS_deg, ...
                     delta_phi_deg, type)
% [R, Q, sigma_deg] = correlation(M, spacing, d_norm,
%                     cluster_number, amplitude_cluster, PAS_type,
%                     phi_deg, AS_deg, delta_phi_deg, type)
%
% Derives the correlation matrix R from the description of the
% environment, namely the antenna element spacing and the way the
% waves impinge (number of clusters, PAS type, AS and mean angle of
% incidence). The generated correlation coefficients are either
% (complex) field correlation coefficients (type = 0) or (real
% positive) power correlation coefficients (type = 1).
%
% Inputs
%
% * Variable M, number of antenna elements of the ULA
% * Variable spacing, spacing of the antenna elements of the ULA
% * Vector d_norm, containing the relative spacings of the M
%   elements of the ULA with respect to the first one
% * Variable cluster_number, number of impinging clusters
% * Vector amplitude_cluster, containing the amplitude of
%   the cluster_number impinging clusters
% * Variable PAS_type, defines the nature of the PAS, uniform
%   (1), Gaussian (2) or Laplacian (3)
% * Vector phi_deg, containing the AoAs of the number_cluster
%   clusters
% * Vector AS_deg, containing the ASs of the number_cluster
%   clusters
% * Vector delta_phi_deg, containing the constraints limits
%   of the truncated PAS, if applicable (Gaussian and Laplacian
%   case)
% * Variable type, defines whether correlation properties
%   should be computed in field (0) or in power (1)
%
% Outputs
%
% * 2-D Hermitian matrix R of size M x M, whose elements are
%   the correlation coefficients of the corresponding elements
%   of the ULA impinged by the described PAS
% * Vector Q of cluster_number elements, giving the normalisation
%   coefficients to be applied to the clusters in order to have
%   the PAS fulfilling the definition of a pdf
% * Vector sigma_deg of cluster_number of elements, giving
%   the standard deviations of the clusters, derived from
%   their description. There is not necessarily equality between
%   the given AS and the standard deviation of the modelling PAS.
%
%
% STANDARD DISCLAIMER
%
% CSys is furnishing this item "as is". CSys does not provide any
% warranty of the item whatsoever, whether express, implied, or
% statutory, including, but not limited to, any warranty of
% merchantability or fitness for a particular purpose or any
% warranty that the contents of the item will be error-free.
%
% In no respect shall CSys incur any liability for any damages,
% including, but limited to, direct, indirect, special, or
% consequential damages arising out of, resulting from, or any way
% connected to the use of the item, whether or not based upon
% warranty, contract, tort, or otherwise; whether or not injury was
% sustained by persons or property or otherwise; and whether or not
% loss was sustained from, or arose out of, the results of, the
% item, or any services that may be provided by CSys.
%
% (c) Laurent Schumacher, AAU-TKN/IES/KOM/CPK/CSys - February 2002

% Normalisation
switch(PAS_type)
    case 1 % Uniform distribution
        Q = normalisation_uniform(cluster_number, ...
					 amplitude_cluster, ...
					 AS_deg);
        sigma_deg = -1; % meaningless in uniform PAS
    case 2 % Gaussian distribution
        [Q, sigma_deg] = ...
	    normalisation_gaussian(cluster_number, ...
				   amplitude_cluster, ...
				   AS_deg, ...
                   delta_phi_deg);
    case 3 % Laplacian distribution
        [Q, sigma_deg] = ...
	    normalisation_laplacian(cluster_number, ...
				    amplitude_cluster, ...
				    AS_deg, ...
                    delta_phi_deg);
    otherwise
	disp('PAS type non supported. Exiting...');
        return
    end;

if (M>1)
    % Complex correlation computation
    switch(PAS_type)
    case 1 % Uniform distribution
        Rxx = bessel(0,2.*pi.*d_norm);
        Rxy = zeros(size(Rxx));
        for k=1:cluster_number
            Rxx = Rxx + Q(k).*Rxx_uniform(d_norm, ...
						  phi_deg(k), ...
						  AS_deg(k));
            Rxy = Rxy + Q(k).*Rxy_uniform(d_norm, ...
						  phi_deg(k), ...
						  AS_deg(k));
        end;
    case 2 % Gaussian distribution
        Rxx = bessel(0,2.*pi.*d_norm);
        Rxy = zeros(size(Rxx));
        for k=1:cluster_number
            Rxx = Rxx + Q(k).*Rxx_gaussian(d_norm, ...
						  phi_deg(k), ...
						  sigma_deg(k), ...
                          delta_phi_deg(k));
            Rxy = Rxy + Q(k).*Rxy_gaussian(d_norm, ...
						  phi_deg(k), ...
						  sigma_deg(k), ...
                          delta_phi_deg(k));
        end;
    case 3 % Laplacian distribution
        Rxx = bessel(0,2.*pi.*d_norm);
        Rxy = zeros(size(Rxx));
        for k=1:cluster_number
            Rxx = Rxx + Q(k).*Rxx_laplacian(d_norm, ...
						  phi_deg(k), ...
						  sigma_deg(k), ...
                          delta_phi_deg(k));
            Rxy = Rxy + Q(k).*Rxy_laplacian(d_norm, ...
						  phi_deg(k), ...
						  sigma_deg(k), ...
                          delta_phi_deg(k));
        end;
    end;
    % Correlation coefficient computation
    if (type == 0)
        tmp = Rxx + i.* Rxy;
    else
        tmp = Rxx.^2 + Rxy.^2;
    end;
    R = toeplitz(tmp);
else
    R = 1;
end;